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Risk, Return, and Ross Recovery

Peter Carr and Jiming Yu
The Journal of Derivatives Fall 2012, 20 (1) 38-59; DOI: https://doi.org/10.3905/jod.2012.20.1.038
Peter Carr
is the executive director of the Masters in Math Finance Program at Courant Institute, New York University in New York, NY.
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  • For correspondence: pcarr@nyc.rr.com
Jiming Yu
is a vice president at a large financial institution in New York, NY.
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Abstract

Carr was asked to share his thoughts on the current state of derivatives theory and practice. His response was to write a discussion and extension of one of the most provocative and potentially important new ideas in the field: Ross’s recent paper on extracting both the risk-neutral density and the empirical density from a set of market option prices. This feat has long been regarded as impossible, so demonstrating that it is not is a major achievement. Carr and Yu detail how the proof is done and then present an alternative route to the same result, but starting from what may be considered a more tractable assumption that a numeraire portfolio exists.

TOPICS: Options, statistical methods

  • © 2012 Pageant Media Ltd
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The Journal of Derivatives: 20 (1)
The Journal of Derivatives
Vol. 20, Issue 1
Fall 2012
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Risk, Return, and Ross Recovery
Peter Carr, Jiming Yu
The Journal of Derivatives Aug 2012, 20 (1) 38-59; DOI: 10.3905/jod.2012.20.1.038

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Risk, Return, and Ross Recovery
Peter Carr, Jiming Yu
The Journal of Derivatives Aug 2012, 20 (1) 38-59; DOI: 10.3905/jod.2012.20.1.038
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  • Article
    • Abstract
    • MATHEMATICAL PRELIMINARY AND ROSS RECOVERY THEOREM
    • MATHEMATICAL PRELIMINARY: REGULAR STURM—LIOUVILLE PROBLEM
    • ASSUMPTIONS OF THE MODEL
    • ANALYSIS
    • AN ILLUSTRATION
    • SUMMARY AND FUTURE RESEARCH
    • ENDNOTES
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